I'm assuming that the decedent died in Texas. When a person dies in Texas without a Will, we apply a set of statutes of descent and distribution, and the situation is commonly referred to as "intestacy." This is the Will written for you by the government, and it's yours until you change it by writing your own Will.
Applying that Will requires at least a little education on our community property principles. Separate property is property that a person acquires before a marriage, or during a marriage by gift or inheritance. Community property is everything else.
Under your facts, the decedent was married with two children from a previous marriage. The community property shared by the decedent and his wife is split down the middle. The surviving spouse retains her one-half of this property, both real and personal. The decedent's half of the community property passes to his children in equal shares. If the decedent owned separate property, it passes in thirds -- 2/3 to his children and 1/3 to his surviving spouse, both real and personal. The catch with separate real property is that the 1/3 that passes to his surviving spouse is ultimately only a life estate. The surviving spouse has the right to live in the home, but at her death or abandonment, the property reverts back to the decedent's children. The link below is provided by the Harris County probate courts, and it often helps explain all of this division.
Our probate laws and homestead provisions can heavily favor a surviving spouse in situations like this, often making things difficult for years when the decedent's children do not have a good relationship with their step-parent. You would be well-advised to encourage your niece to locate an experienced probate attorney near her to walk her through what is likely going to happen next.
I see that you're posting from Mount Vernon, which is not all too far from my Dallas/Fort Worth practice area. If you'd like, I wouldn't mind elaborating on my answer and pointing you in the right direction. Feel free to contact me through the link below or through my profile on this site.
This answer does not constitute legal advice. I am admitted to practice law in the State of Texas only, and make no attempt to opine on matters of law that are not relevant to Texas. This answer is based on general principles of law that may or may not relate to your specific situation, and is for promotional purposes only. You should never rely on this answer alone and nothing in these communications creates an attorney-client relationship.
This is why it is so important to get proper estate planning accomplished!
Maybe the State of Texas' solution would be just fine with your dad, maybe (probably?) not; but who knows and it's too late now...
Don't let that happen to you, when visiting my colleague on your dad's case, why not get yours done too? And drag your spouse along with you!